Factor a^4-16

Problem

a4−16

Solution

1. Identify the expression as a difference of squares, which follows the pattern x2−y2=(x−y)*(x+y)

2. Rewrite the terms as squares of simpler expressions.

a4=(a2)2

16=4

3. Apply the formula for the difference of squares using x=a2 and y=4

a4−16=(a2−4)*(a2+4)

4. Identify that the first factor (a2−4) is also a difference of squares.

a2−4=a2−2

5. Apply the formula again to the factor (a2−4)

a2−4=(a−2)*(a+2)

6. Combine all factors into the final expression. Note that (a2+4) is a sum of squares and cannot be factored further using real numbers.

Final Answer

a4−16=(a−2)*(a+2)*(a2+4)

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